"A restaurant owner said that the total of a meal is 600$ for 20 people. For every additonal client in the group, there will be a 1$ deduction for the individual price". What is the maximum profit that this owner can get?
I'm having problems with this. Keep in mind that this is tenth grade quadratic systems...
I'm having problems with this. Keep in mind that this is tenth grade quadratic systems...
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Total meal for 20 people is 20*30= 600
Let x be additional people over 20
So total people= 20+x
Price = 30-x
Total of meal = (20+x)(30-x)= -x^2+10x +600
This is a parabola that opens down. The vertex represents the maximum.
X= -b/(2a)= -10/(-2)= 5
The max occurs when there are 5 extra people, which is 25 people, who would pay 30-5= 25 dollars each.
Cost = 25*25= 625 dollars
Hoping this helps!
Let x be additional people over 20
So total people= 20+x
Price = 30-x
Total of meal = (20+x)(30-x)= -x^2+10x +600
This is a parabola that opens down. The vertex represents the maximum.
X= -b/(2a)= -10/(-2)= 5
The max occurs when there are 5 extra people, which is 25 people, who would pay 30-5= 25 dollars each.
Cost = 25*25= 625 dollars
Hoping this helps!
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price per person at 20 people = 600/20 = $30
Let p = # of people above 20 and f(p) = price for p people beyond 20.
f(p) = (20 + p)(30 - p) = 600 + 10p - p^2
f(p) has a maximum where f '(p) = 0 and f ''(p) < 0.
f '(p) = 10 - 2p
0 = 10 - 2p
p = 5
f ''(p) = -2 < 0 for all p so we know the maximum occus at p = 5.
Maximum profit = f(5) = 25(25) = $625
Let p = # of people above 20 and f(p) = price for p people beyond 20.
f(p) = (20 + p)(30 - p) = 600 + 10p - p^2
f(p) has a maximum where f '(p) = 0 and f ''(p) < 0.
f '(p) = 10 - 2p
0 = 10 - 2p
p = 5
f ''(p) = -2 < 0 for all p so we know the maximum occus at p = 5.
Maximum profit = f(5) = 25(25) = $625